Question

In Young's double slit, 18 fringes are observed to be formed in a certain segment of the screen when light of wavelength 400 nm is used. If the wavelength is changed to 600 nm, the number of fringes observed in the same segment of the screen is

• A. \(6\)
• B. \(12\)
• C. \(18\)
• D. \(24\)

Hint:

Fringe width is proportional to the wavelength, so the number of fringes in a fixed segment is inversely proportional to the wavelength.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
In Young's double slit experiment the fringe width is \(\beta=\dfrac{\lambda D}{d}\). For the same set-up only \(\lambda\) changes, so \(\beta\propto\lambda\).

Step 2: Fringes in a fixed segment
If the segment has length \(L\), the number of fringes is \(N=\dfrac{L}{\beta}\propto\dfrac{1}{\lambda}\). Hence \(N_1\lambda_1=N_2\lambda_2\).

Step 3: Calculation
\(18\times 400=N_2\times 600\)
\(N_2=\dfrac{7200}{600}=12\).

Final Answer:
The number of fringes in the same segment becomes 12. \[ \boxed{\text{(B) }12} \]